I'm going to write it out and actually this might remind you of unit analysis that you might do when you first did unit conversion but it also works out here. So this is.now I think we are ready to start converting. So you would get pi/180 radians is equal to 1 degree. So all I did is I divided both sides by (pi) and if you wanted to figure out how many radians are there per degree you can divide both sides by 180. So if you divide both sides of this by (pi), you would get one radian it would have to go from plural to singular one radian is equal to 180/pi degrees. And if you wanna really think about, well how many degrees are there per radian you can divide both sides of this by (pi). The arc that subtends that angle is (pi) radiusssses and that's also 180 degrees. And you can have (pi) radians are equal to 180 degrees or another way to think about it going halfway around a circle in radians is (pi) radians. And this is really enough information for us to think about how to convert between radians and degrees if we want to simplify this a little bit we can divide both sides by 2. I can either write it with the little degree symbol like that or I can write it just like that. If I do one revolution of a circle how many radians is that going to be? Well we know one revolution of a circle is (2)(pi) radians and how many degrees is that if I do one revolution around a circle? Well we know that is 360 degrees. And just as a review lets just remind ourselves the relationship and I always do this before I have to convert between the two. Lets see if we can give ourselves a little bit of practice converting between radians and degrees and degrees and radians. and as you said, it is not a perfect defined answer and is not theoretically accurate. This gives you a perfect theortical answer. Circumference of a circle of diameter 3 is 3π. When you find the circumference of a rocket, you may need more accuracy.īut of course, theoretically we can still get a definite answer if we just dont expand π and leave it as π. If you want to find the circumference of a random cart wheel, you dont need accuracy. Instead we have to estimate to the accuracy required for the situation. Theoretically in math, since we always use rational numbers most of the time, an irrational number like pi is often confusing as it does not provide a definite rational answer. So, every answer may continue on forever, but what we estimate, is what we need practically. We are always estimating because the exact amount is almost never needed, and we take as accurate a measurement as required. A pencil said to be 8 cm long may be 8.000034 cm for example. Take a measurement of a length of anything, we won't get an exact whole number.
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